Related papers: Growing Scale-free Networks by a Mediation-Driven …
In this paper, we first discuss the origin of preferential attachment. Then we establish the generalized preferential attachment which has two new properties; first, it encapsulates both the topological and weight aspects of a network,…
This paper presents a tighter bound on the degree distribution of arbitrary P\'{o}lya urn graph processes, proving that the proportion of vertices with degree $d$ obeys a power-law distribution $P(d) \propto d^{-\gamma}$ for $d \leq…
We consider a growing network, whose growth algorithm is based on the preferential attachment typical for scale-free constructions, but where the long-range bonds are disadvantaged. Thus, the probability to get connected to a site at…
In this contribution we introduce local attachment as an universal network-joining protocol for peer-to-peer networks, social networks, or other kinds of networks. Based on this protocol nodes in a finite-size network dynamically create…
Global degree/strength based preferential attachment is widely used as an evolution mechanism of networks. But it is hard to believe that any individual can get global information and shape the network architecture based on it. In this…
Preferential attachment is widely used to model power-law behavior of degree distributions in both directed and undirected networks. In a directed preferential attachment model, despite the well-known marginal power-law degree…
In this paper, a random graph process ${G(t)}_{t\geq 1}$ is studied and its degree sequence is analyzed. Let $(W_t)_{t\geq 1}$ be an i.i.d. sequence. The graph process is defined so that, at each integer time $t$, a new vertex, with $W_t$…
In this paper, a directed network model for world-wide web is presented. The out-degree of the added nodes are supposed to be scale-free and its mean value is $m$. This model exhibits small-world effect, which means the corresponding…
We obtain the degree distribution for a class of growing network models on flat and curved spaces. These models evolve by preferential attachment weighted by a function of the distance between nodes. The degree distribution of these models…
We study the following paradox associated with networks growing according to superlinear preferential attachment: superlinear preference cannot produce scale-free networks in the thermodynamic limit, but there are superlinearly growing…
In spite of its relevance to the origin of complex networks, the interplay between form and function and its role during network formation remains largely unexplored. While recent studies introduce dynamics by considering rewiring processes…
We present a simple mechanism for generating undirected scale-free networks using random walkers, where the network growth is determined by choosing parent vertices by sequential random walks. We show that this mechanism produces scale-free…
We study structural properties of trees grown by preferential attachment. In this mechanism, nodes are added sequentially and attached to existing nodes at a rate that is strictly proportional to the degree. We classify nodes by their depth…
Empirical evidence suggests that heavy-tailed degree distributions occurring in many real networks are well-approximated by power laws with exponents $\eta$ that may take values either less than and greater than two. Models based on various…
Large real-world networks typically follow a power-law degree distribution. To study such networks, numerous random graph models have been proposed. However, real-world networks are not drawn at random. Therefore, Brach, Cygan, {\L}acki,…
We study the Krapivsky-Redner (KR) network growth model but where new nodes can connect to any number of existing nodes, $m$, picked from a power-law distribution $p(m)\sim m^{-\alpha}$. Each of the $m$ new connections is still carried out…
Our work introduces an approach for estimating the contribution of attachment mechanisms to the formation of growing networks. We present a generic model in which growth is driven by the continuous attachment of new nodes according to…
We introduce a collection of complex networks generated by a combination of preferential attachment and a previously unexamined process of "splitting" nodes of degree $k$ into $k$ nodes of degree 1. Four networks are considered, each…
We introduce the notion of globally updating evolution for a class of weighted networks, in which the weight of a link is characterized by the amount of data packet transport flowing through it. By noting that the packet transport over the…
In most networks, the connection between a pair of nodes is the result of their mutual affinity and attachment. In this letter, we will propose a Mutual Attraction Model to characterize weighted evolving networks. By introducing the initial…